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A Story about Absolutely Nothing

This article for the young and old talks about the origins of our number system and the important role zero has to play in it.

Balance Power

Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?

Galley Division

Can you explain how Galley Division works?

Arrow Arithmetic 1

Age 14 to 16
Challenge Level

Emanuel has yet another set of solutions to these 3 problems. He ignores the length of the arrows but uses the direction! I suspect that completes the set of plausible solutions here.

We will ignore the length of an arrow in order to simplify the problem. Basing on traditional number line an arrow pointing upwards or to the right can represent a plus (+), and an arrow pointing downwards or the left can represent a minus (-).

From above the answer for question 1 is 3.

The first arrow of question 2 can represent 0 because it is halfway between +1 and 1.
The second arrow is -1 and the third also is 0 since its halfway between 1 and -1.
The result for question 2 therefore is -1

The third question is actually -1 + 1 which is 0.

Can you now interpret Sam, Tim and Hannah's solutions according to whether they pay attention to arrow length and arrow direction or not?